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On an infinite dimensional linear-quadratic problem with fixed endpoints: The continuity question Cover

On an infinite dimensional linear-quadratic problem with fixed endpoints: The continuity question

Open Access
|Dec 2014

References

  1. Athans, M. (1971). The role and use of the stochastic linear-quadratic-Gaussian problem in control system design, IEEE Transactions on Automatic Control, AC-16(6): 529-552.10.1109/TAC.1971.1099818
  2. Aubin, J.-P. (2000). Applied Functional Analysis, Wiley, New York, NY.10.1002/9781118032725
  3. Balakrishnan, A.V. (1981). Applied Functional Analysis, Springer, New York, NY.
  4. Brockett, R.F. (1970). Finite-Dimensional Linear Systems, Wiley, New York, NY.
  5. Chow, G.P. (1976). Analysis and Control of Dynamic Economic Systems, Wiley, New York, NY.
  6. Corless, M.J. and Frazho, A.E. (2003). Linear Systems and Control.10.1201/9780203911372
  7. An Operator Perspective, Marcel Dekker, New York, NY.
  8. Curtain, R.F. (1984). Linear-quadratic control problem with fixed endpoints in infinite dimensions, Journal of Optimization Theory and Its Applications 44(1): 55-74.10.1007/BF00934894
  9. Curtain, R.F. and Pritchard A.J. (1978). Infinite-Dimensional Linear Systems Theory, Springer, Berlin.10.1007/BFb0006761
  10. Curtain, R.F. and Zwart H. (1995). An Introduction to Infinite- Dimensional Linear Systems Theory, Springer, New York, NY.10.1007/978-1-4612-4224-6
  11. Douglas, R.G. (1966). On majorization, factorization, and range inclusion of operators on Hilbert space, Proceedings of the American Mathematical Society 18(2): 413-415.10.1090/S0002-9939-1966-0203464-1
  12. Emirsajłow, Z. (1989). Feedback control in LQCP with a terminal inequality constraint, Journal of Optimization Theory and Applications 62(3): 387-403.10.1007/BF00939813
  13. Evans, L.C. (2010). Partial Differential Equations, American Mathematical Society, Providence RI.
  14. Federico, S. (2011). A stochastic control problem with delay arising in a pension fund model, Finance and Stochastics 15(3): 421-459.10.1007/s00780-010-0146-4
  15. Fuhrmann, P.A. (1972). On weak and strong reachability and controllability of infinite-dimensional linear systems, Journal of Optimization Theory and Its Applications 9(2): 77-89.10.1007/BF00932345
  16. Kandilakis, D. and Papageorgiou, N.S. (1992). Evolution inclusions of the subdifferential type depending on a parameter, Commentationes Mathematicae Universitatis Carolinae 33(3): 437-449.
  17. Kendrick, D.A. (1981). Stochastic Control for Economic Models, McGraw-Hill, New York, NY.
  18. Kobayashi, T. (1978). Some remarks on controllability for distributed parameter systems, SIAM Journal on Control and Optimization 16(5): 733-742.10.1137/0316049
  19. Laurent, P.-J. (1972). Approximation et Optimisation, Hermann, Paris.
  20. Ljungqvist, L. and Sargent, T.J. (2004). Recursive Macroeconomic Theory, MIT Press, Cambridge, MA.
  21. Luenberger, D.G. (1969). Optimization by Vector Space Methods, Wiley, New York, NY.
  22. Papageorgiou, N.S. (1991). On the dependence of the solutions and optimal solutions of control problems on the control constraint set, Journal of Mathematical Analysis and Applications 158(2): 427-447.10.1016/0022-247X(91)90247-W
  23. Porter, W.A. (1966). Modern Foundations of System Engineering, Macmillan, New York, NY.
  24. Przyłuski, K.M. (1981). Remarks on continuous dependence of an optimal control on parameters, in O. Moeschlin and D. Pallaschke (Eds.), Game Theory and Mathematical Economics, North-Holland, Amsterdam, pp. 333-337.
  25. Rolewicz, S. (1987). Functional Analysis and Control Theory. Linear Systems, PWN, Warsaw, (in Polish).10.1007/978-94-015-7758-8
  26. Sent, E.-M. (1998). The Evolving Rationality of Rational Expectations: An Assessment of Thomas Sargent’s Achievements, Cambridge University Press, Cambridge.10.1017/CBO9780511528514
  27. Triggiani, R. (1975a). A note on the lack of exact controllability for mild solutions in Banach spaces, SIAMJournal on Control and Optimization 15(3): 407-411.10.1137/0315028
  28. Triggiani, R. (1975b). On the lack of exact controllability for mild solutions in Banach spaces, Journal of Mathematical Analysis and Applications 50(2): 438-446.10.1016/0022-247X(75)90033-5
  29. Triggiani, R. (1976). Extensions of rank conditions for controllability and observability to Banach spaces and unbounded operators, SIAM Journal on Control and Optimization 14(2): 313-338. 10.1137/0314022
DOI: https://doi.org/10.2478/amcs-2014-0053 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 723 - 733
Submitted on: Sep 30, 2013
Published on: Dec 20, 2014
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2014 K.Maciej Przyłuski, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.